\newproblem{lay:7_1_27}{
  % Problem identification
	\begin{large}
	  \hspace{\fill}\newline
    \textbf{Lay, 7.1.27}
	\end{large}
	\\
  \ifthenelse{\boolean{identifyAuthor}}{\textit{Carlos Oscar Sorzano, Aug. 31st, 2013} \\}{}

  % Problem statement
	Suppose $A$ is a symmetric $n\times n$ matrix and $B$ is any $n\times m$ matrix. Show that $B^TAB$, $B^TB$ and $BB^T$ are symmetric matrices.
}{
   % Solution
	Let's calculate the transpose of each one of the matrices and show that they are equal to the original matrices
	\begin{center}
		$(B^TAB)^T=B^TA^T(B^T)^T=B^TAB$ \\
		$(B^TB)^T=B^T(B^T)^T=B^TB$\\
		$(BB^T)^T=(B^T)^TB^T=BB^T$
	\end{center}
}
\useproblem{lay:7_1_27}
\ifthenelse{\boolean{eachProblemInOnePage}}{\newpage}{}

